The nature of the three-minute and five-minute oscillations observed in sunspots is considered to be an effect of propagation of magnetohydrodynamic (MHD) waves from the photosphere to the solar corona. However, the real modes of these waves and the nature of the filters that result in rather narrow frequency bands of these modes are still far from being generally accepted in spite of a large amount of observational material obtained in a wide range of wave bands of observations. The significance of this field of research is based on the hope that local seismology can be used to find the structure of the solar atmosphere in magnetic tubes of sunspots. We expect that substantial progress can be achieved by simultaneous observations of the sunspot oscillations in different layers of the solar atmosphere in order to gain information on propagating waves. In this study we used a new method that combines the results of an oscillation study made in optical and radio observations. The optical spectral measurements in photospheric and chromospheric lines of the line-of-sight velocity were carried out at the Sayan Solar Observatory. The radio maps of the Sun were obtained with the Nobeyama Radioheliograph at 1.76 cm. Radio sources associated with the sunspots were analyzed to study the oscillation processes in the chromospherecorona transition region in the layer with magnetic field B = 2000 G. A high level of instability of the oscillations in the optical and radio data was found. We used a wavelet analysis for the spectra. The best similarities of the spectra of oscillations obtained by the two methods were detected in the three-minute oscillations inside the sunspot umbra for the dates when the active regions were situated near the center of the solar disk. A comparison of the wavelet spectra for optical and radio observations showed a time delay of about 50 seconds of the radio results with respect to optical ones. This implies a MHD wave traveling upward inside the umbral magnetic tube of the sunspot. For the five-minute oscillations the similarity in spectral details could be found only for optical oscillations at the chromospheric level in the umbra region or very close to it. The time delays seem to be similar. Besides three-minute and five-minute ones, oscillations with longer periods (8 and 15 minutes) were detected in optical and radio records. Their nature still requires further observational and theoretical study though for even a preliminary discussion.

Long-term oscillations of microwave emission generated in sunspot magnetospheres are detected with the Nobeyama Radioheliograph (NoRH) at a frequency of 17 GHz, and the Siberian Solar Radio Telescope (SSRT) at 5.7 GHz. Significant periodicities in the range of 22-170 min are found in the variation of the emission intensity, polarisation and the degree of circular polarisation. Periods of the oscillations are not stable: they are different in different sunspots and in the same sunspot on different days. A cross-correlation analysis shows the presence of common significant periods in both NoRH and SSRT data. The cross-correlation coefficients are typically lower than 0.5, which can be attributed to the different heights of the emission formation, and different mechanisms for the emission generation (gyroresonance and thermal bremstrahlung at 17 GHz, and pure gyroresonance at 5.7 GHz). The observational results are consistent with the global sunspot oscillation model.

We present an investigation of oscillatory processes with periods in the range of several tens of minutes for some single sunspots of a new solar cycle, observed in 2010-2011 at the same time intervals in the optical and radio ranges. We used magnetograms from SDO/HMI with a cadence of 45 s, and radio images at a frequency of 17 GHz obtained with the Nobeyama Radioheliograph (NoRH). Radio images in intensity (Stokes parameter I ) and circular polarization (Stokes parameter V ) were synthesized with a cadence of ten seconds and ten-second averaging. Time profiles obtained with NoRH and SDO/HMI show a correlation between the radio emission of sunspots and a magnetic field. Wavelet spectra and cross-wavelet transforms give similar oscillation periods: 30-40 min, 60-70 min, 100-110 min, and 150-200 min. The same periods found by fundamentally different methods from ground-based and space observations confirm the solar nature of these oscillations. One of the possible interpretations of our results is that detected oscillations reflect eigen oscillations of a sunspot as a whole predicted by the shallow sunspot model.

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The study of solar radio emission in a wide (covering many octaves) wavelength range is of great importance for plasma diagnostics of all types of solar activity. Here we describe a new spectroanalyzer covering a wide range in frequency from 1 to 18 GHz, which is used at the RATAN-600 radio telescope beginning 1991 December 20. Coronal magnetic fields have been measured with the various radio astronomical methods presented in these proceedings by Gelfreikh et al. and Bogod et al.Of special value are collaborative spectral-polarization observations using the RATAN-600 and high-spatial resolution observations with the VLA and WSRT (Akhmedov et al. 1986; Bogod et al. 1992; Alissandrakis et al. 1992).